FLAT PLATE AND FLAT SLAB CONSTRUCTION

Neil M. Hawkins, Professor Emeritus, University of Illinois

A Tribute to the Lasting Contributions and Legacy of Our

Friend And Colleague Dr. W Gene Corley

ACI Convention, Phoenix, AZ , Sunday October 20, 2013

DISCUSSION TOPICSGene’s Early Professional Years

• Equivalent Frame AnalysisSRS 218 Univ. of Illinois – Ph.D. Thesis –June 1961

ACI Journal – Nov. 1970 – w. James Jirsa

Concrete International – Dec. 1983- w. Dan Vanderbilt

• Testing and Analysis of Flat Plate and Flat Slab System Shear Strengths

ACI Journal Sept.1971- NY World’s Fair Waffle Slab Tests- with DM

ACI Journal – Oct. 1968- Shearhead Reinforcement – w. NMH

ACI SP-30 –1971–Moment and Shear Transfer to Columns–w. NMH

ACI SP-42- 1974- Moment Transfer with Shearheads – w. NMH

WCEE 1973–Ductile Flat-Plate Structures to Resist EQ–w.JEC & PHK

ACI SP-59- 1979– Shear in Two-Way Slabs – ACI Approach

EARLY PROFESSIONAL YEARS

National Science Foundation Fellow 1958-1961

Ph.D Structural Engineering, University of Illinois, 1961

US Army Corps of Engineers, 1961-1964

Structural Research Manager, PCA R & D Division 1964 - 1972

EQUIVALENT FRAME ANALYSIS FOR FLAT PLATES AND FLAT SLABS

• First introduced in ACI 318-71 and based on U of I Ph. D theses by

Corley (1961) and Jirsa (1963).

• Early ACI Codes permitted an “empirical method” of design only; Slab

properties were restricted to those load tested in the early 1900s.

• .

To overcome that restriction the 1941

ACI code introduced an

“elastic design method” giving

similar results to the “empirical method”

for the loaded tested floors but useable

for slabs with dissimilar properties

The 71 Code frame similar to the 41

Code frame except for stiffness

definitions for frame members

1971 AND 1941 DEFORMATION ASSUMPTIONS

1971 SLAB STIFFNESS ASSUMPTIONS

TORSIONAL MEMBER STIFFNESS ASSUMPTIONS

Where C = Torsional Constant

In Corley’s thesis the unit twisting

moment, Fig 3(B), was uniform over the

length L2. Jirsa modified Corley’s

distribution to that shown based on

pattern loading considerations

EQUIVALENT COLUMN STIFFNESS

For moment distribution

procedures the equivalent

column stiffness Kec was

defined by:

1/ Kec = 1/ Kc + 1/ Kt

Kc = column flexural stiffness

Kt = torsional stiffness of

members framing into column

LAYOUT OF 9 PANEL U of I ¼ SCALE MODEL

COMPARISON OF MEASURED AND COMPUTED SERVICE LOAD MOMENTS

COMPARISON WITH PCA

¾ SCALE FLAT PLATE

RESULTS

EQUIVALENT FRAME PROCEDURE LIMITATIONS

Discussed in “ Frame Analysis of Concrete Buildings”

Vanderbilt and Corley, Concrete International, Dec. 1983

• Method assumes analysis by moment distribution methods.

• Method calibrated for gravity loadings only by comparison

to U of I ¼ scale and PCA ¾ scale tests

• Method based on stiffness of uncracked sections

• Method not calibrated for lateral loadings but theoretical

studies suggest using a cracked section stiffness equal to

1/3rd uncracked section stiffness. See ACI 318R13.5.1.2

• The method is extensively used and remains essentially

unchanged since 1971.

PUNCHING SHEAR

• Flat plate for PCA and U of I tests designed for 70 psf LL and 86 psf DL. Grade 40 steel: 3000 psi concrete.

• Both slabs failed by punching at an interior column. Strains in the top steel at the column face ≥ 7 times the yield strain at punching. Failure load of 369 psf and was only 85% of the ACI 4√f’c value.

• Computed yield line strength was 350psf. Based on shape of the load-slab midspan deflection curves and the limited spread of reinforcement yielding across the width of the slab a capacity greater than the 369psf was likely if not for the punching failure.

• Punching was classified as a “secondary” failure due to the extensive yielding of the top reinforcement around the column prior to failure.

PUNCHING SHEAR ISSUES

• How to prevent the “secondary” punching failure

and enable large slab deflections before failure?

Answer: Shear reinforcement but what type?

• How to evaluate punching strength when there is

also moment being transferred from slab to

column?

• Under Gene’s leadership PCA set out to make

significant contributions to addressing both

those issues.

SHEAR REINFORCEMENT STUDIESShearheads

1930 Wheeler Patent Shearhead

PCA TEST SPECIMENS 1966 PCA TEST SHEARHEADS

SHEAR REINFORCEMENT STUDIES10 Specimens with Shearheads Tested

Ls = 0 Ls = 18 in Ls = 20 in

Shearhead increases shear capacity in the same way as a larger column.

For warning of failure shearhead should yield before punching.

Then critical section for shear does not extend to end of shearhead

SHEAR REINFORCEMENT STUDIESShearhead – Determination of Required Capacity

SHEAR DETERMINED FROM

STRAIN GAGE READINGS

IDEALIZED SHEAR

K= EI OF SHEARHEAD

EI COMPOSITE SECTION

WIDTH (c + d) K ≥ 0.15

SHEAR REINFORCEMENT STUDIESShearhead – Location of Critical Section for Shear

SHEAR REINFORCEMENT STUDIESShear and Moment Transfer – Existing ACI Code

Additional “v” Caused by M

Fraction γf Mu to be transferred by flexure

within lines 1.5h either side of column

where

and b1 = c1 + d

For RC slabs and exterior columns γf can be

increased to 1.0 provided Vu does not exceed

0.75ϕVc for edge columns and 0.50 ϕVc for

corner columns. At interior columns γf can be

increased by 25% but to not greater than 1.0

provided Vu ≤ 0.40 ϕVc and εt ≥ 0.010.

Determining Fraction of M Transferred

by Reinforcement

UNDERSTANDING SHEAR AND MOMENT TRANSFERBEAM ANALOGY

Model Torsional, Flexural and Overall Response

UNDERSTANDING SHEAR AND MOMENT TRANSFERBEAM ANALOGY - EXTERIOR COLUMN STRENGTH

SHEAR REINFORCEMENT STUDIES Exterior Column Connections -Dimensions

VARIABLES:

Sheahead - Shape, Length, Area

Column Size -3 with 12 x 8 in

-11 with 12 x 12 in

Grade 60 Steel

Sanded Lightweight Concrete 3,000 psi

SHEAR REINFORCEMENT STUDIESExterior Column Connections – Test Setup

SHEAR REINFORCEMENT STUDIESExterior Column Connections – Loading Response

D = 12 x 8; C = 12 x12 column

N = No Shearhead

C = Channel Sections

H = I Sections

Under-reinforced CH4; CC5; DC2

Projections: 17.5; 21; 21 in

Over-reinforced CH1,2,3

Projections: 8.5, 11.5, 14.5 in

Over-reinforced CT1, CC1, CC2

Projections: 14.5, 21, 21 in

SHEAR REINFORCEMENT STUDIESExterior Column Connections – Critical Sections

For shear stress v1 due to Shear

For shear stress v2 due to Moment Transfer

For Design v1 + v2 = vu ≤ ϕ vn

SHEAR REINFORCEMENT STUDIESExterior Column Connections – Shearhead Strength

Requirements

Current Code Requirement For Plastic Moment Strength

WHAT STILL NEEDS TO BE ADDRESSED?Slabs Without Shear Reinforcement – Flexural Strength Limit

• Recognize Relevance of Muttoni’s

Critical Shear Crack (CSC) Theory

• Aggregate Interlock Along CSC Is

Lost When There Is General

Yielding of Reinforcement in the

Vicinity of Column

• Per Ghali, Strength for General

Yielding is 8m where m is flexural

strength per unit width

• Require ϕvVshear≤ ϕf Vflex = ϕf 8m –

Needed for low ρ

WHAT STILL NEEDS TO BE ADDRESSED?Slabs Without Shear Reinforcement – Depth Effect

kv = 3/√d

WHAT STILL NEEDS TO BE ADDRESSED?Slabs With Shear Reinforcement

• Develop Conceptually Consistent Punching Shear,

Moment Transfer, and Ductility Provisions For

Connections With Shear Reinforcement

Cover Stirrup Reinforcement,

Stud Rail Reinforcement,

Fortress Reinforcement,

Shearhead Reinforcement.

Thank You